geometry section 0-9 1112
TRANSCRIPT
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Section 0-9Square Roots and Simplifying Radicals
Tuesday, September 20, 2011
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Essential Question
How do you evaluate square roots and simplify radical expressions?
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Vocabulary
1. Product Property:
2. Quotient Property:
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Vocabulary
1. Product Property: For two numbers a and b ≥ 0,
ab = ai b
2. Quotient Property:
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Vocabulary
1. Product Property: For two numbers a and b ≥ 0,
ab = ai b
2. Quotient Property: For two numbers a and b ≥ 0,
ab
=a
b
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Example 1Simplify.
a. 54 b. 126
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Example 1Simplify.
a. 54 b. 126
9i7
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Example 1Simplify.
a. 54 b. 126
9i7
9i 7
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Example 1Simplify.
a. 54 b. 126
9i7
9i 7
3 7
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Example 1Simplify.
a. 54 b. 126
9i7
9i 7
3 7
9i14
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Example 1Simplify.
a. 54 b. 126
9i7
9i 7
3 7
9i14
9i 14
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Example 1Simplify.
a. 54 b. 126
9i7
9i 7
3 7
9i14
9i 14
3 14
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Example 2Simplify.
a. 80x7y3z4 b. 25a12r8t11
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Example 2Simplify.
a. 80x7y3z4 b. 25a12r8t11
16i5ix6ixiy2iyiz4
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Example 2Simplify.
a. 80x7y3z4 b. 25a12r8t11
16i5ix6ixiy2iyiz4
4 x3 yz4 5xy
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Example 2Simplify.
a. 80x7y3z4 b. 25a12r8t11
16i5ix6ixiy2iyiz4
4 x3 yz4 5xy
25ia12ir8it10it
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Example 2Simplify.
a. 80x7y3z4 b. 25a12r8t11
16i5ix6ixiy2iyiz4
4 x3 yz4 5xy
25ia12ir8it10it
5a6r4 t 5 14
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Example 3Simplify.
a. 25
49 b. 81
16
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Example 3Simplify.
a. 25
49
25
49
b. 81
16
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Example 3Simplify.
a. 25
49
25
49
57
b. 81
16
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Example 3Simplify.
a. 25
49
25
49
57
b. 81
16
81
16
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Example 3Simplify.
a. 25
49
25
49
57
b. 81
16
81
16
94
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Example 4Simplify.
a. 7
5 b. 9
12
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Example 4Simplify.
a. 7
5
7
5i
5
5
b. 9
12
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Example 4Simplify.
a. 7
5
7
5i
5
5
7 55
b. 9
12
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Example 4Simplify.
a. 7
5
7
5i
5
5
7 55
b. 9
12
9
12i
12
12
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Example 4Simplify.
a. 7
5
7
5i
5
5
7 55
b. 9
12
9
12i
12
12
9 1212
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Example 4Simplify.
a. 7
5
7
5i
5
5
7 55
b. 9
12
9
12i
12
12
9 1212
9 4i312
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Example 4Simplify.
a. 7
5
7
5i
5
5
7 55
b. 9
12
9
12i
12
12
9 1212
9 4i312
18 312
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Example 4Simplify.
a. 7
5
7
5i
5
5
7 55
b. 9
12
9
12i
12
12
9 1212
9 4i312
18 312
3 32
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Example 5Simplify.
a. 4
1− 7 i1+ 7
1+ 7
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Example 5Simplify.
a. 4
1− 7 i1+ 7
1+ 7
4(1+ 7)
(1− 7)(1+ 7)
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Example 5Simplify.
a. 4
1− 7 i1+ 7
1+ 7
4(1+ 7)
(1− 7)(1+ 7)
4(1+ 7)
(1− 7)(1+ 7)Tuesday, September 20, 2011
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Example 5Simplify.
a. 4
1− 7 i1+ 7
1+ 7
4(1+ 7)
(1− 7)(1+ 7)
4(1+ 7)
(1− 7)(1+ 7)
4 + 4 7
1− 7 + 7 − 7
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Example 5Simplify.
a. 4
1− 7 i1+ 7
1+ 7
4(1+ 7)
(1− 7)(1+ 7)
4(1+ 7)
(1− 7)(1+ 7)
4 + 4 7
1− 7 + 7 − 7
4 + 4 7−6
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Example 5Simplify.
a. 4
1− 7 i1+ 7
1+ 7
4(1+ 7)
(1− 7)(1+ 7)
4(1+ 7)
(1− 7)(1+ 7)
4 + 4 7
1− 7 + 7 − 7
4 + 4 7−6
2 + 2 7−3
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Example 5Simplify.
b. 5
6 + 8 i6 − 8
6 − 8
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Example 5Simplify.
b. 5
6 + 8 i6 − 8
6 − 8
5(6 − 8)
(6 + 8)(6 − 8)
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Example 5Simplify.
b. 5
6 + 8 i6 − 8
6 − 8
5(6 − 8)
(6 + 8)(6 − 8)
30 − 5 8
6 + 8 − 8 − 8Tuesday, September 20, 2011
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Example 5Simplify.
b. 5
6 + 8 i6 − 8
6 − 8
5(6 − 8)
(6 + 8)(6 − 8)
30 − 5 8
6 + 8 − 8 − 8
30 − 5 4i236 − 8
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Example 5Simplify.
b. 5
6 + 8 i6 − 8
6 − 8
5(6 − 8)
(6 + 8)(6 − 8)
30 − 5 8
6 + 8 − 8 − 8
30 − 5 4i236 − 8
30 −10 228
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Example 5Simplify.
b. 5
6 + 8 i6 − 8
6 − 8
5(6 − 8)
(6 + 8)(6 − 8)
30 − 5 8
6 + 8 − 8 − 8
30 − 5 4i236 − 8
30 −10 228
15 − 5 214
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Problem Set
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Problem Set
p. P20 1-20 all
“Hold yourself responsible for a higher standard than anyone else expects of you. Never excuse yourself.” - Henry Ward Beecher
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